That is not the final answer, you need to solve considering the different intervals.

With algebrator you have arrived to the following equation:

It needs further solving by using the definition for absolute value.

For the interval (-~, -2) U (2, + ~) we have 

For the interval (-2, 2) we have

You can also solve the above equation by graphing and finding the intersection with x-axis.

Click here to see the graph.

Another, more simple way is to replace (x-2)(x+2) by 'y' and solve:

This way, you need to solve:

That is for, y > = 0 (that is x in the interval (-~, -2)U(2, +~)) it is 

And the solutions is 3/2.

Click here to see the solving.

Now, go back to solving 

(x - 2)(x + 2) = 3/2

........

Click here to see to solving

........

See the above graph, it is exactly the same solution.

For y < 0  (that is x in the interval (-2, 2)) it is

The solution is complex, thus we have no real solutions for 'x' for this interval.

Finally, we can conclude that the only real solutions are: